Which of the following numbers is a factor of 133? ${7,10,11,12,13}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $133$ by each of our answer choices. $133 \div 7 = 19$ $133 \div 10 = 13\text{ R }3$ $133 \div 11 = 12\text{ R }1$ $133 \div 12 = 11\text{ R }1$ $133 \div 13 = 10\text{ R }3$ The only answer choice that divides into $133$ with no remainder is $7$ $ 19$ $7$ $133$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $133$ $133 = 7\times19 7 = 7$ Therefore the only factor of $133$ out of our choices is $7$. We can say that $133$ is divisible by $7$.